Syntax

Description

dCV = dcovary(nfactors,fixed) uses
a coordinate-exchange algorithm to generate a D-optimal
design for a linear additive model with nfactors factors,
subject to the constraint that the model include the fixed covariate
factors in fixed. The number of runs in the design
is the number of rows in fixed. The design dCV augments fixed with
initial columns for treatments of the model terms.

[dCV,X] = dcovary(nfactors,fixed) also
returns the design matrix X associated with the
design.

[dCV,X] = dcovary(nfactors,fixed,model) uses
the linear regression model specified in model. model is
one of the following strings:

'linear' — Constant and
linear terms. This is the default.

'interaction' — Constant,
linear, and interaction terms

'quadratic' — Constant,
linear, interaction, and squared terms

'purequadratic' — Constant,
linear, and squared terms

The order of the columns of X for a full
quadratic model with n terms is:

Alternatively, model can be a matrix
specifying polynomial terms of arbitrary order. In this case, model should
have one column for each factor and one row for each term in the model.
The entries in any row of model are powers
for the factors in the columns. For example, if a model has factors X1, X2,
and X3, then a row [0 1 2] in model specifies
the term (X1.^0).*(X2.^1).*(X3.^2). A row of all
zeros in model specifies a constant term,
which can be omitted.

[dCV,X] = daugment(...,param1,val1,param2,val2,...) specifies
additional parameter/value pairs for the design. Valid parameters
and their values are listed in the following table.

Parameter

Value

'bounds'

Lower and upper bounds for each factor, specified as
a 2-by-nfactors matrix. Alternatively,
this value can be a cell array containing nfactors elements,
each element specifying the vector of allowable values for the corresponding
factor.

'categorical'

Indices of categorical predictors.

'display'

Either 'on' or 'off' to
control display of the iteration counter. The default is 'on'.

'excludefun'

Handle to a function that excludes undesirable runs.
If the function is f, it must support the syntax b = f(S),
where S is a matrix of treatments with nfactors columns
and b is a vector of Boolean values with the same
number of rows as S. b(i)
is true if the ith row S should
be excluded.

'init'

Initial design as an mruns-by-nfactors matrix.
The default is a randomly selected set of points.

'levels'

Vector of number of levels for each factor.

'maxiter'

Maximum number of iterations. The default is 10.

'options'

The value is a structure that contains options specifying
whether to compute multiple tries in parallel, and specifying how
to use random numbers when generating the starting points for the
tries. Create the options structure with statset.
Applicable statset parameters are:

'UseParallel' — If true and
if a parpool of the Parallel Computing Toolbox™ is
open, compute in parallel. If the Parallel Computing Toolbox is
not installed, or a parpool is not open, computation
occurs in serial mode. Default is false, meaning
serial computation.

UseSubstreams — Set to true to
compute in parallel in a reproducible fashion. Default is false.
To compute reproducibly, set Streams to a type
allowing substreams: 'mlfg6331_64' or 'mrg32k3a'.

Streams — A RandStream object or cell array of such
objects. If you do not specify Streams, dcovary uses
the default stream or streams. If you choose to specify Streams,
use a single object except in the case

You have an open Parallel pool

UseParallel is true

UseSubstreams is false

In that case, use a cell array the same size as the
Parallel pool.

'tries'

Number of times to try to generate a design from a new
starting point. The algorithm uses random points for each try, except
possibly the first. The default is 1.

Examples

Example 1

Suppose you want a design to estimate the parameters in a three-factor
linear additive model, with eight runs that necessarily occur at different
times. If the process experiences temporal linear drift, you may want
to include the run time as a variable in the model. Produce the design
as follows:

The column vector time is a fixed factor,
normalized to values between ±1. The number
of rows in the fixed factor specifies the number of runs in the design.
The resulting design dCV gives factor settings
for the three controlled model factors at each time.

Example 2

The following example uses the dummyvar function
to block an eight-run experiment into 4 blocks of size 2 for estimating
a linear additive model with two factors: